Drying Constant
k = 1.62 x 10-10 ps2.233
Robert C. Hansen and Harold M. Keener,
Department of Food, Agricultural, and Biological Engineering,
Ohio Agricultural Research and Development Center,
The Ohio State University,
Wooster, Ohio.
Paper No. 936032. Written for presentation at the 1993 International Summer Meeting sponsored by the American Society of Agricultural Engineers and the Canadian Society of Agricultural Engineering. Spokane Center, Spokane, Washington. June 20-23, 1993. Reprinted with permission.
The ornamental yew, Taxus x media 'Hicksii,' has been identified as a renewable source of Taxol. However, clippings from the plant must be properly and efficiently harvested, dried, and stored.
Analysis of deep bed drying systems for Taxus plant material was done using the logarithmic model of drying. Results show drying capacity, airflow, energy costs, and efficiency as a function of fan power and bed depth.
Ornamental yews are pruned on an annual basis as a part of standard nursery practices. Pruning typically occurs either in April/May or September/October. For commercial Taxol production, the clippings must be properly and efficiently harvested, dried, and stored. Hansen et al. (1993) have published data on thin-layer drying of Taxus and showed 50° to 60°C gave high rates of drying with no loss in Taxol yield. However, no published data exist on the optimum airflows and depth that would be energy efficient and cost effective for drying Taxus material.
The objective of this research was to evaluate and optimize airflow rate and bed depth as design parameters for minimizing cost of drying Taxus plant material.
Sabbah et al. (1979) reported that the analytic model described as a logarithmic model application to deep bed drying (Hukill, 1954; Barre et al., 1971) could be used to predict average drying-time history and forecast the average moisture content of a deep bed of grain dried with ambient or solar-heated air. This model was used in this study instead of finite difference models of grain drying (Morey et al., 1978; Bakker-Arkema et al., 1978; Keener et al., 1978), because of computational speed and flexibility in solving for optimum dryer designs.
The equations used to analyze for time to dry a batch (or bin) of product from initial moisture Mo to final moisture Mf and to calculate the energy cost per ton of grain dried (see Nomenclature on page 65), were:
| Average Moisture Ratio |
(1) |
|
Drying Constant k = 1.62 x 10-10 ps2.233 |
(2) |
| Depth Unit
|
(3) |
| Time to Dry |
(4) |
| Equilibrium Moisture |
(5) |
Analysis for efficiency of drying requires knowledge of parameter values and average weather conditions for Ohio. Keener et al. (1981) defined energy conversion values used in efficiency analysis. Hansen et al. (1993) collected thin-layer drying data. Evaluation of Me for Taxol was based on relative humidity levels of three percent. Average weather conditions for Wooster, Ohio, are 15.6°C dry bulb and 8.8°C dew point in May and 11.7°C dry bulb and 6.4°C dew point in October.
The computer program used was written in FORTRAN IV and run on an HP-3000 computer system. The program contains:
In the computer program, iterations are performed on airflow until a minimum energy to dry the product is found. Output is optimum airflow rate and product depth to minimize energy as a function of fan power and drying air temperature.
For Taxus material, maximum depth for the analysis was limited to 10 ft. because of practical considerations pertaining to loading clippings into and out of bins. As a result, optimization was not attained. However, useful information was provided by the program by simulating specific drying conditions.
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| Figure 1. Drying capacity vs. fan size as a function of bed depth for drying Taxus clippings using a plenum temperature of 60°C and air conditions reflecting north-central Ohio in May (15.6°C dry bulb and 8.8°C dew point). |
Figure 2. Specific airflow rate vs. fan size as a function of bed depth for drying Taxus clippings using a plenum temperature of 60°C and air conditions reflecting north- central Ohio in May (15.6°C dry bulb and 8.8°C dew point). |
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| Figure 3. Energy cost vs. fan size as a function of bed depth for drying Taxus clippings using a plenum temperature of 60°C and air conditions reflecting north- central Ohio in May (15.6°C dry bulb and 8.8°C dew point). |
Figure 4. Drying efficiency vs. fan size as a function of bed depth for drying Taxus clippings using a plenum temperature of 60°C and air conditions reflecting north- central Ohio in May (15.6°C dry bulb and 8.8°C dew point). |
In this report, drying (fossil fuel) efficiency is defined as the ratio of latent heat in the water evaporated to the fossil-fuel energy input. Because electrical power generation and delivery is approximately 33 percent efficient in terms of energy conversion, the electrical energy was converted to a fossil-fuel equivalent by multiplying by a factor of three. Similarly, LP gas was converted to a fossil-fuel equivalent by dividing by a factor of 0.90 for its energy conversion ratio.
Based on a plenum temperature of 60°C and average weather conditions for north central Ohio in May, Figures 1, 2, 3, and 4 can be used to predict drying capacities, specific airflow rates, energy costs, and drying efficiencies for drying Taxus clippings as a function of fan size and bed depth. Use of these simulated results can be illustrated with an example.
Suppose rate of harvest and allowable storage time for fresh-cut Taxus clippings required a drying capacity of 267 kg/hr. Also, assume a standard 27-ft.-diameter grain bin with a 15-hp fan was available (floor area equals 16.2 m2). By dividing 267 kg/hr. by 16.2 m2, drying capacity requirements can be estimated at 16.5 kg/hr/m2. A 15-hp fan is roughly equivalent to 1 kW/m2. Figure 1 can now be used to select a bed depth of 8.5 ft.
Figure 2 can be used to estimate required airflow. Using 1 kW/m2 and a depth of 8.5 ft., specific airflow rate is shown as 10 m3/s/t. Similarly, based on these same criteria, Figure 3 shows cost of energy for drying Taxus clippings would be about $0.007/kg (dry basis), and Figure 4 shows drying efficiency would be 0.1 kg of water per MJ of energy.
The significance of the effect of bed depth on drying conditions is shown by decreasing depth from 8.5 ft. to 7 ft. Based on a specific airflow requirement of 10 m3/s/t, Figure 2 shows the fan size is now cut in half to 0.5 kW/m2. Similarly, Figure 1 shows drying capacity will be reduced to 13.5 kg/hr/m2 (dry basis) while drying efficiency (Figure 4) drops to 0.085 kg of water per MJ of energy.
A logarithmic drying model developed for grain drying was adapted for use in predicting expected drying results for Taxus clippings. Results of the simulation were displayed graphically, showing drying capacity, airflow, energy costs, and drying efficiency as a function of fan size and bed depth. An example of a drying situation is described, showing how simulation results can be used to predict the effects of varying bed depth based on a plenum temperature of 60°C.
Bakker-Arkema, F. W., R. C. Brook, and L. E. Lerew. 1978. Cereal grain drying. In: Advances in Cereal Science and Technology. Vol. II. Y. Pemeranz, Ed. American Association of Cereal Chemists, Inc. St. Paul, Minn. pp. 1-90.
Barre, H. J., G. R. Gaughman, and M. Y. Hamdy. 1971. Application of the logarithmic model to cross-flow deep-bed grain drying. Transactions of the ASAE. 14(6): 1061-1064.
Croom, E. M. Jr., H. N. ElSohly, T. R. Sharpe, and J. D. McChesney. 1991. Research Institute of Pharmaceutical Sciences. School of Pharmacy. The University of Mississippi. Private communication.
Hansen, R. C., H. M. Keener, and H. N. ElSohly. 1993. Thin-layer drying of cultivated Taxus clippings. Transactions of the ASAE. 36(6):1873-1877.
Hukill, W. V. 1954. Grain drying. AACC Monograph II. Storage of cereal grains. American Association of Cereal Chemists. St. Paul, Minn. pp. 402-485.
Keener, H. M., T. L. Glenn, and R. N. Misra. 1981. Minimizing fossil-fuel energy in corn drying systems. Transactions of the ASAE. 24(5): 1357-1362, 1366.
Keener, H. M., G. E. Meyer, M. A. Sabbah, and R. B. Curry. 1978. Simulation of solar grain drying. Agricultural Engineering Series 102. Ohio Agricultural Research and Development Center. The Ohio State University. Wooster, Ohio.
Morey, R. V., H. M. Keener, T. L. Thompson, G. M. White, and F. W. Bakker-Arkema. 1978. The present status of grain drying simulation. ASAE Paper No. 78-3009. American Society of Agricultural Engineers. St. Joseph, Mich.
Sabbah, M. A., H. M. Keener, and G. E. Meyer. 1979. Simulation of solar drying of shelled corn using the logarithmic model. Transactions of the ASAE. 22(3): 637-643.
Witherup, K. M., S. A. Look, M. W. Stasko, T. J. Ghiorzi, and G. M. Muschik. 1990. Taxus spp. needles contain amounts of Taxol comparable to the bark of Taxus brevifolia: analysis and isolation. Journal of Natural Products. 53(5): 1249-1255.
Ca = specific heat of air, kJ kg-10C-1)
D = depth unit of the bed, dimensionless
k = drying constant, h-1
L = latent heat of moisture evaporation, kJ/kg
Mf = average moisture content of the bed, decimal dry basis
Me = equilibrium moisture content, decimal dry basis
Mo = initial moisture content, decimal dry basis
MR = average moisture ratio of the bed, decimal dimensionless
ps = vapor pressure at saturation, Pa
q = airflow, m3/s (at STP)
ra = air density, kg/m3
rg = material bulk density, kg/m3
RH = relative humidity
Tg = temperature of material, °C
Te = outlet air temperature at equilibrium with the grain in the downstream; for sufficiently deep bed, Te is equivalent to the wet bulb temperature, °C
To = time-averaged drying temperature, °C
Y = bed depth, m
td = drying time, h